I can`t afford to attend University, so am trying to teach myself a degree in maths - or at least to be able to read degree level maths. The available textbooks, even for year 1, are extremely difficult and tedious for me. With videos such as these the fog begins, slowly, to lift.
I’ve been exactly we’re your starting from, just wanted to encourage you to keep at it and go into a local community college one day and ask about potential ways to attend. I did one class at a time at first. Salute, best of luck.
These are the basics I've been looking for but missed somewhere along the line, this visualization helps not only with math, but also explains some simple ideas I have encountered with 3d modeling. Didn't imagine Linear Algebra could be so closely related to 3D, silly really, but I'm here because the examples used in a lecture to explain 3 variables in 3 dimensional space left me totally confused. EDIT: I had to add that this is exactly what I needed to start getting a handle on this. Really looking forward to chewing over this and then moving on to your other videos, thanks again.
Sir you took away my burden to understand plane in 3d. Sir your efforts in creating such visualizing mathematical video is marvelous I recommend if you could do visualizing videos for math topics seems complicated to understand, this is because I realized that understanding visually is more beneficial than memorizing math formula.
Thank you so much.... Now I know I actually understood nothing in my lecture. This really helped. Its hard to understand planes without a proper visual representation.
The creators of Why U have been hard at work for a number of months now on a series of lectures that cover the topics of exponential and logarithmic functions. We still have a few months to go to complete these animated lectures! - Professor V.S.
@@MyWhyU That is so good to know kind Sir. I thought you guys gave the world a glimpse into how educational content ought to be and then dipped. Couldn't find any of the names on Linkedin. Why is this ORG so low profile!!
I know this maybe childish but can you please post a video about the "multiplication using the hands trick," when it come to tutorials in mathematics this channel is the only one i can trust. thank you
How about hyperplanes ? Can we visualise hyperplanes in such kind of framework as you constructed here ? If not, how can we find solutions involving scenarios of some higher order abstractions ?
Great question! In fact, we are currently in the process of finishing "Algebra Chapter 82 - Complex Functions" that addresses several methods of creating graphs that would normally require 4 dimensions to visualize.
"The points where all three planes simultaneously intersect correspond to solutions which simultaneously satisfy all three equations. These points, therefore, correspond to the solution of the system. I wonder how can I explain these sentences philosophically to myself. Beyond the equality of any two expressions, (or six expressions in three equations), in an equation. Thank you.
Hello Arif: If x + y = 3 then any combination of values of x and y must always add up to three. For example, when x is three then y is zero, and when y is three then x is zero.
why eliminating one of the variables in a 2 variable linear equation would allow the eliminated variable to take on any value? Can someone give me some pointers please.
you dont eliminate the variable, because the constant is zero, no matter what value the variable takes on, it doesn't have an effect on the outcome of the equation. so the constant is zero and this allows the variable to move freely without having any influence
when you have something like 0x + By = C, it doesn't matter what the value of x is, the 0x term will always have a value of 0 because 0 times anything is 0. so, x can be absolutely anything; it will be multiplied by 0 in the 0x term so the term will always equal 0.
An equation of two or more variables defines a relationship between all the variables in the equation, so unless stated otherwise, none of the variables in an equation are independent. On the other hand, a mathematical function is a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
@@MyWhyU Can one say that the standard form of an equation in three variables is just a manipulation of a function in two variables? And if so, then what is the significance of designating one as a "function" specially when their graphs are always the same at least when the variables degree is one?
Each unknown variable would require its own dimension, so 4 unknowns would need to be visualized in 4-dimensional space, etc. That becomes a challenge for 3-dimensional creatures like ourselves!
@@Celenova i was wondering where would i place 4th dimension suppose time be 4th dimension and the 3 dimensions are mutually perpendicular so we want a space where we could put this 4th dimension t so that all 4 are mutually perpendicular and would you agree with me lets assume the 4th dimension will make a plane that covers itself completely . like a cube
No, if you graphed a system of 4 equations with 4 variables that's when you start thinking in terms of cubes, if you graphed a system of 4 equations with 3 variables it would still be 4 planes and the intersecting point is the solution
The complex plane is 2-dimensional. Normally the horizontal axis corresponds to the real part of the complex number and the vertical axis corresponds to the imaginary part of the complex number. To plot the input versus output of a complex function you would need 4 dimensions - two for the input values and two for the output values.
Sir!! For Values of X=0 and Y=0 then only Z=any constant value...then how you can conclude that in representation in graph for Z=any constant...X and Y will be any value of real numbers...It should be 0 only for both the values x and y🙄
It sounds like you may be confusing the values of the variables x and y with the coefficients A and B of x and y. You are correct that if x = 0, y = 0, and z = some constant value "c", then the only point that satisfies that would be a single point lying on the z-axis (0, 0, c) . However, if the coefficients A and B of x and y are both zero then x and y can have any value, since they are both multiplied by zero and therefore don't effect the result.
yeah , I also get it now , you was wrong with variables ..A and B are constants ..not variables. ! or your input values.., which means you are allowed to have equation 2x+3y+1z = D ..that's not wrong but all such equations will eventually become Z = 3 lines ., which will create a z plane because you can satisfy z =3 for any x , y values..so it'll eventually make a plane.
There are many theories about the origins of Professor Von Schmohawk. Many of them are only conjecture or hearsay. Some clues to his origin may possibly lie in Pre-Algebra Chapter 1 - "The Dawn of Numbers".
I can't believe I finally understand planes. Thank you very much for the visuals! You're truly a life saver
I was desperately looking for a good explanation and finally found it, Thank you
I can`t afford to attend University, so am trying to teach myself a degree in maths - or at least to be able to read degree level maths. The available textbooks, even for year 1, are extremely difficult and tedious for me. With videos such as these the fog begins, slowly, to lift.
Hey mate, I hope you're doing well.
I’ve been exactly we’re your starting from, just wanted to encourage you to keep at it and go into a local community college one day and ask about potential ways to attend. I did one class at a time at first. Salute, best of luck.
न्क्स्ग्क्स्ग्क्स्ग्क्स्क्स्क्स्न्क्स्क्स्क्स्न्क्स्क्स्क्स्न्द्द
Keep it up mate, I highly appreciate your dedication and effort towards seeking knowledge ;)))
Same here. I keep looking for resources and lots out there
These are the basics I've been looking for but missed somewhere along the line, this visualization helps not only with math, but also explains some simple ideas I have encountered with 3d modeling. Didn't imagine Linear Algebra could be so closely related to 3D, silly really, but I'm here because the examples used in a lecture to explain 3 variables in 3 dimensional space left me totally confused. EDIT: I had to add that this is exactly what I needed to start getting a handle on this. Really looking forward to chewing over this and then moving on to your other videos, thanks again.
Sir you took away my burden to understand plane in 3d. Sir your efforts in creating such visualizing mathematical video is marvelous I recommend if you could do visualizing videos for math topics seems complicated to understand, this is because I realized that understanding visually is more beneficial than memorizing math formula.
Thank you so much.... Now I know I actually understood nothing in my lecture. This really helped. Its hard to understand planes without a proper visual representation.
This really helped me understand the required form for a 2D plane jn 3D!!! Thank you!
This is the best video I have seen so far explaining Linear algebra visually
Thanks a lot sir!!!
You cannot imagine how many student's life you have saved....
Thank you so much for the videos
This channel deserves million of subscribers!❤️🇵🇰
Thank you so much. Much love from India
Awesome! hope this team produces whole range of Math videos in future, I'm ready to buy even if it has a cost.
why are you not making videos ? your visualization is awesome take other math topics such as statistics, probability, and calculus
The creators of Why U have been hard at work for a number of months now on a series of lectures that cover the topics of exponential and logarithmic functions. We still have a few months to go to complete these animated lectures! - Professor V.S.
@@MyWhyU That is so good to know kind Sir. I thought you guys gave the world a glimpse into how educational content ought to be and then dipped. Couldn't find any of the names on Linkedin. Why is this ORG so low profile!!
Great content and AWESOME graphics!!!!
Thanks so much for this video. You explained everything so simply and clearly!
this couldn't be any more clear...mind blowing
Mister all I can say to you is, wow! Thank you so much for this. As soon as I start making some money again, I am sending you some.❣
this is so helpful and also very entertaining to watch, thanks for making this vid!!
Incredibly useful and clear. Thank you for providing this great resource.
I know this maybe childish but can you please post a video about the "multiplication using the hands trick," when it come to tutorials in mathematics this channel is the only one i can trust. thank you
Amazing and very easy to understand video!
A perfect visualization. Just what I was looking for!
5:40 thats why 3eqn forms a plane very very brilliant explanation sir thankyou sm
Thanks for placing those images in my mind!
What about a system of equation like y=2x? Can you describe that on a 3d-plane.
Simply draw the graph of y = 2x on the xy-plane and then extend every point on that line vertically up and down into the z dimension to form a plane.
Really great explanation! Thanks a lot.
How about hyperplanes ? Can we visualise hyperplanes in such kind of framework as you constructed here ? If not, how can we find solutions involving scenarios of some higher order abstractions ?
Great question! In fact, we are currently in the process of finishing "Algebra Chapter 82 - Complex Functions" that addresses several methods of creating graphs that would normally require 4 dimensions to visualize.
Great as always, keep up the good work 👍
Animations are so cute 😭❤️
How about in 4d Space?
"The points where all three planes simultaneously intersect correspond to solutions which simultaneously satisfy all three equations. These points, therefore, correspond to the solution of the system.
I wonder how can I explain these sentences philosophically to myself. Beyond the equality of any two expressions, (or six expressions in three equations), in an equation. Thank you.
EXCELLENT CLASS, SIR
This is so cute and informative, THANK YOU!!!
hi, how x+y can be three when, it seems from the graph, x is 3 and y is 3? thank you for that wonderful teaching.
Hello Arif: If x + y = 3 then any combination of values of x and y must always add up to three. For example, when x is three then y is zero, and when y is three then x is zero.
I have a question
Solving linear equations in 3 variables graphically is only possible on a computer/laptop?
yes
Just a good job of turning the things in my head into equations on the screen.
why eliminating one of the variables in a 2 variable linear equation would allow the eliminated variable to take on any value? Can someone give me some pointers please.
you dont eliminate the variable, because the constant is zero, no matter what value the variable takes on, it doesn't have an effect on the outcome of the equation. so the constant is zero and this allows the variable to move freely without having any influence
when you have something like 0x + By = C, it doesn't matter what the value of x is, the 0x term will always have a value of 0 because 0 times anything is 0. so, x can be absolutely anything; it will be multiplied by 0 in the 0x term so the term will always equal 0.
Is there a name given to this process of setting a variable to 0, it is the first time I'm coming across this. It is quite confusing.
My like was the 1000th :D
So gratifying to see 999 turning into 1K
Does the standard form eliminate the dependent-independent relationship between variables? This is realy confusing to me!
An equation of two or more variables defines a relationship between all the variables in the equation, so unless stated otherwise, none of the variables in an equation are independent. On the other hand, a mathematical function is a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
@@MyWhyU Can one say that the standard form of an equation in three variables is just a manipulation of a function in two variables? And if so, then what is the significance of designating one as a "function" specially when their graphs are always the same at least when the variables degree is one?
I appreciate the effort on the british accent, but it's so obvious that your'e american in some parts XD
+Rachael Alexander His origins are very mysterious.
+MyWhyU Haha XD
Wow
I just imagine that if I try to make such a video how much efforts I have to take
what would a plane of y=z look like?
That would be a plane that includes both the x-axis and the line "y = z; x = any constant".
this plane equation?
amazing explanation thank you!
what if there are 4 unknowns, what does it reperesents? or 5 or more
Each unknown variable would require its own dimension, so 4 unknowns would need to be visualized in 4-dimensional space, etc. That becomes a challenge for 3-dimensional creatures like ourselves!
@@MyWhyU thanks a lot
@@MyWhyU yea it's impossible for human brains to visualise 4 dimensions so any equations with 4 or 4+ cannot be solved by graphical method
@@Celenova i was wondering where would i place 4th dimension suppose time be 4th dimension and the 3 dimensions are mutually perpendicular so we want a space where we could put this 4th dimension t so that all 4 are mutually perpendicular
and would you agree with me lets assume the 4th dimension will make a plane that covers itself completely . like a cube
@@Celenova and can you see that the line which intersect in 3D plane that line will become a plane in 4th dimension
I love your lecture
thank you
brilliant. first class.
Very Good video. Thank You so much.
this was very entertaining to watch
thanks I finally understand
Thanku sir ❤❤ it's help lot
So wait if you graphed a system of 4 equations, wouldn’t it just make 4 cubes where all centers of the cube meet?
That's what I'm wandering
No, if you graphed a system of 4 equations with 4 variables that's when you start thinking in terms of cubes, if you graphed a system of 4 equations with 3 variables it would still be 4 planes and the intersecting point is the solution
Great explanation
Very helpful!
I love these.
thank you so much!
Very helpful.
That yell at 6:40 was hilarious!
is this the same 3d visualisation that we need to use for a complex plane for imaginary numbers???
The complex plane is 2-dimensional. Normally the horizontal axis corresponds to the real part of the complex number and the vertical axis corresponds to the imaginary part of the complex number. To plot the input versus output of a complex function you would need 4 dimensions - two for the input values and two for the output values.
Thanks a lot Sir
Sir!!
For Values of X=0 and Y=0 then only Z=any constant value...then how you can conclude that in representation in graph for Z=any constant...X and Y will be any value of real numbers...It should be 0 only for both the values x and y🙄
It sounds like you may be confusing the values of the variables x and y with the coefficients A and B of x and y. You are correct that if x = 0, y = 0, and z = some constant value "c", then the only point that satisfies that would be a single point lying on the z-axis (0, 0, c) . However, if the coefficients A and B of x and y are both zero then x and y can have any value, since they are both multiplied by zero and therefore don't effect the result.
yeah , I also get it now , you was wrong with variables ..A and B are constants ..not variables. ! or your input values.., which means you are allowed to have equation 2x+3y+1z = D ..that's not wrong but all such equations will eventually become Z = 3 lines ., which will create a z plane because you can satisfy z =3 for any x , y values..so it'll eventually make a plane.
Where's professor von schmohawk from? His accent is untraceable.
There are many theories about the origins of Professor Von Schmohawk. Many of them are only conjecture or hearsay. Some clues to his origin may possibly lie in Pre-Algebra Chapter 1 - "The Dawn of Numbers".
ScuderiaPhineasRacin I am, he is not.
+morgengabe1 Sounds like a dude from Boston/New York doing a really bad british accent... very curious...
6:03 funny sound effect😂😂
👀🙏🙌🧘🤸💕💕
Nice
Best
Best